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A166634 Totally multiplicative sequence with a(p) = 4*(p-1) for prime p. 3
1, 4, 8, 16, 16, 32, 24, 64, 64, 64, 40, 128, 48, 96, 128, 256, 64, 256, 72, 256, 192, 160, 88, 512, 256, 192, 512, 384, 112, 512, 120, 1024, 320, 256, 384, 1024, 144, 288, 384, 1024, 160, 768, 168, 640, 1024, 352, 184, 2048, 576, 1024 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
Multiplicative with a(p^e) = (4*(p-1))^e. If n = Product p(k)^e(k) then a(n) = Product (4*(p(k)-1)^e(k).
a(n) = A165825(n) * A003958(n) = 4^bigomega(n) * A003958(n) = 4^A001222(n) * A003958(n).
MATHEMATICA
DirichletInverse[f_][1] = 1/f[1]; DirichletInverse[f_][n_] :=
DirichletInverse[f][n] = -1/f[1]*Sum[f[n/d]*DirichletInverse[f][d], {d, Most[Divisors[n]]}]; muphi[n_] := MoebiusMu[n]*EulerPhi[n]; a[m_] := DirichletInverse[muphi][m]; Table[a[m]*4^(PrimeOmega[m]), {m, 1, 100}] (* G. C. Greubel, May 20 2016 *)
f[p_, e_] := (4*(p-1))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 17 2023 *)
PROG
(PARI) a(n) = {my(f = factor(n)); for (k=1, #f~, f[k, 1] = 4*(f[k, 1]-1)); factorback(f); } \\ Michel Marcus, May 20 2016
CROSSREFS
Sequence in context: A312762 A312763 A312764 * A189007 A242349 A309521
KEYWORD
nonn,easy,mult
AUTHOR
Jaroslav Krizek, Oct 18 2009
STATUS
approved

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Last modified June 21 08:06 EDT 2024. Contains 373543 sequences. (Running on oeis4.)